minus, 4, left parenthesis, minus, 8, w, minus, 4, x, right parenthesis, minus, 7, x, minus, 10, left parenthesis, minus, 10, x, plus, 8, w, right parenthesis−4(−8w−4x)−7x−10(−10x+8w)

Let's simplify the expression step by step:

Given:
\[
-4(-8w - 4x) - 7x - 10(-10x + 8w)
\]

### Step 1: Distribute the factors.

First, distribute \(-4\) to both terms inside the first parentheses:
\[
-4(-8w - 4x) = (32w + 16x)
\]

Next, distribute \(-10\) to both terms inside the second parentheses:
\[
-10(-10x + 8w) = (100x - 80w)
\]

Now substitute these into the original expression:
\[
32w + 16x - 7x + 100x - 80w
\]

### Step 2: Combine like terms.

For the \(w\) terms:
\[
32w - 80w = -48w
\]

For the \(x\) terms:
\[
16x - 7x + 100x = 109x
\]

### Final Expression:
\[
-48w + 109x
\]

This is the simplified form of the expression.

Would you like further details on any steps or have any questions?

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**Relative Questions:**
1. How do we apply the distributive property?
2. What are like terms, and why can we combine them?
3. Can the order of terms affect the result in addition and subtraction?
4. How would this expression change if we added another variable term?
5. How does factoring differ from distributing?

**Tip:** Always distribute negative signs carefully to avoid errors in simplification.

In this example, learn how to simplify the algebraic expression −4(−8w−4x)−7x−10(−10x+8w) using the distributive property. Step-by-step instructions cover key algebraic concepts such as distributing negative factors and combining like terms. Suitable for students in Grades 8-10.

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